# Alphabetical list for input.neo¶

## ANISO_MODEL_*¶

Definition

Parameter which selects whether to treat a species with an anisotropic temperature model.

Choices

• ANISO_MODEL_*=1: isotropic temperature model

• ANISO_MODEL_*=2: anisotropic temperature model

• This option is presently not available for experimental profiles (PROFILE_MODEL = 2).

• This model requires ROTATION_MODEL = 2 due to the induced poloidal density asymmetry.

• The parallel and perpendicular temperature TEMP_PARA_* and TEMP_PERP_* and the parallel and perpendicular temperature gradient scale lengths DLNTDR_PARA_* and DLNTDR_PERP_* must also be set.

• The parameters TEMP_* and DLNTDR_* are not used. The effective Maxwellian temperature in the DKE is determined internally based on the parallel and perpendicular temperatures.

• DEFAULT: 1

• The anisotropic model of each species 1-11 is set as: ANISO_MODEL_1, ANISO_MODEL_2, ANISO_MODEL_3,…

• The subroutine interface parameter is specified as a vector: neo_aniso_model_in(1:11)

## BETA_STAR¶

Definition

$\beta_* = - \frac{8\pi a}{B_{\rm unit}^2} \sum_a \frac{d p_a}{d r}$

where $$B_{\rm unit}(r)=(q/r)\psi^\prime$$ is the effective magnetic field strength and $$p=\sum_a n_a T_a$$ is the total plasma pressure.

• DEFAULT: 0.0

• NOTE: This parameter is not used in the standard DKE equation! It is only used in the case of an anisotropic temperature species (e.g. ANISO_MODEL_* = 2) to compute $$d\Phi_*/dr$$.

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), $$\beta_*$$ is computed internally from the profile parameters in input.profiles and the normalizing length scale is the plasma minor radius.

## BTCCW¶

Definition

Parameter which selects the orientation of the toroidal magnetic field $$B_t$$ relative to the toroidal angle $$\varphi$$.

Choices

• BTCCW = 1: Counter-clockwise when viewed from above the torus - negative $$\hat{e}_{\varphi}$$ for the right-handed coordinate system $$(r,\theta,\varphi)$$. Thus, $$B_t$$ is oriented along the negative $$\hat{e}_{\varphi}$$ direction.

• BTCCW = -1: Clockwise when viewed from above the torus - positive $$\hat{e}_{\varphi}$$ for the right-handed coordinate system $$(r,\theta,\varphi)$$. Thus, $$B_t$$ is oriented along the positive $$\hat{e}_{\varphi}$$ direction.

• DEFAULT: -1

• In DIII-D, typically BTCCW = 1.

• When experimental profiles are used (PROFILE_MODEL = 2), the orientiation of BT is inferred from input.profiles.

## COLLISION_MODEL¶

Definition

Parameter which selects the collision operator model.

Choices

• SIM_MODEL = 1: Connor model.

• SIM_MODEL = 2: Zeroth-order Hirshman-Sigmar model.

• SIM_MODEL = 3: Full Hirshman-Sigmar model.

• SIM_MODEL = 4: Full linearized Fokker-Plank operator.

• SIM_MODEL = 5: FP test particle operator with ad hoc field particle operator.

• DEFAULT: 4

## DELTA¶

Definition

Average triangularity, $$\delta$$, of the flux surface:

$\delta = \frac{\delta_{+} + \delta_{-}}{2}$

where $$\delta_{+}$$ is the upper triangularity and $$\delta_{-}$$ is the lower triangularity.

• DEFAULT: 0.0

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the triangularity as a function of radius is read from input.profiles.

## DENS_*¶

Definition

The normalized equilibrium-scale density:

${\rm DENS}\_* = \frac{n_{*}}{n_{\rm norm}}$

Commments

• DEFAULT: DENS_1=1.0, DENS_2=DENS_3=…=0.0

• The density of each species 1-11 is set as: DENS_1, DENS_2, DENS_3,…

• When experimental profiles are used (PROFILE_MODEL = 2), the density as a function of radius is read from input.profiles and the normalizing density is the local density of Species 1, $$n_{\rm norm}(r)=n_{0,{\rm species 1}}$$.

• When rotation effects are included (ROTATION_MODEL = 2), this parameter is the value at the outboard midplane ($$\theta=0$$).

• The subroutine interface parameter is specified as a vector: neo_dens_in(1:11)

## DLNNDR_*¶

Definition

The normalized equilibrium-scale density gradient scale length:

${\rm DLNNDR}\_* = -a \frac{\partial {\rm ln} n_{*}}{\partial r}$

Commments

• DEFAULT: 1.0

• The density gradient scale length of each species 1-11 is set as: DLNNDR_1, DLNNDR_2, DLNNDR_3,…

• When experimental profiles are used (PROFILE_MODEL = 2), the density as a function of radius is read from input.profiles and the density gradient is computed internally. The normalizing length is the plasma minor radius.

• When rotation effects are included (ROTATION_MODEL = 2), this parameter is the value at the outboard midplane ($$\theta=0$$).

• The subroutine interface parameter is specified as a vector: neo_dlnndr_in(1:11)

Definition

The normalized equilibrium-scale density gradient scale length of the electrons for the case of adiabatic electrons:

${\rm DLNNDRE\_ADE} = -a \frac{\partial {\rm ln} n_{0,e}}{\partial r}$

Commments

• DEFAULT: 1.0

• This parameter does not enter the DKE and is used only as a diagnostic for strong rotation (ref:neo_rotation_model = 2), for which it is the value at the outboard midplane ($$\theta=0$$).

• This paramter is used only if no species with Z < 0 is specified.

• When experimental profiles are used (PROFILE_MODEL = 2), the density as a function of radius is read from input.profiles and the density gradient is computed internally. The normalizing length is the plasma minor radius.

## DLNTDR_*¶

Definition

The normalized equilibrium-scale temperature gradient scale length:

${\rm DLNTDR}\_* = -a \frac{d {\rm ln} T_{*}}{d r}$

Commments

• DEFAULT: 1.0

• The temperature gradient scale length of each species 1-11 is set as: DLNTDR_1, DLNTDR_2, DLNTDR_3,…

• When experimental profiles are used (PROFILE_MODEL = 2), the temperature as a function of radius is read from input.profiles and the temperature gradient is computed internally. The normalizing length is the plasma minor radius.

• The subroutine interface parameter is specified as a vector: neo_dlntdr_in(1:11)

## DLNTDR_PARA_*¶

Definition

The normalized equilibrium-scale parallel temperature gradient scale length:

${\rm DLNTDR}\_PARA\_* = -a \frac{d {\rm ln} T_{\|,*}}{d r}$

Commments

• DEFAULT: 1.0

• The parallel temperature gradient scale length of each species 1-11 is set as: DLNTDR_PARA_1, DLNTDR_PARA_2, DLNTDR_PARA_3,…

• This parameter is used only when the species’ anisotropic flag is set (ANISO_MODEL_* = 2).

• The subroutine interface parameter is specified as a vector: neo_dlntdr_para_in(1:11)

## DLNTDR_PERP_*¶

Definition

The normalized equilibrium-scale perpendicular temperature gradient scale length:

${\rm DLNTDR}\_PERP\_* = -a \frac{d {\rm ln} T_{\perp,*}}{d r}$

Commments

• DEFAULT: 1.0

• The perpendicular temperature gradient scale length of each species 1-11 is set as: DLNTDR_PERP_1, DLNTDR_PERP_2, DLNTDR_PERP_3,…

• This parameter is used only when the species’ anisotropic flag is set (ANISO_MODEL_* = 2).

• The subroutine interface parameter is specified as a vector: neo_dlntdr_perp_in(1:11)

Definition

The normalized equilibrium-scale temperature gradient scale length of the electrons for the case of adiabatic electrons:

${\rm DLNTDRE\_ADE} = -a \frac{\partial {\rm ln} T_{e}}{\partial r}$

Commments

• DEFAULT: 1.0

• This parameter does not enter the DKE and is used only as a diagnostic for strong rotation (ref:neo_rotation_model = 2), for which it is the value at the outboard midplane ($$\theta=0$$).

• This paramter is used only if no species with Z < 0 is specified.

• When experimental profiles are used (PROFILE_MODEL = 2), the temperature as a function of radius is read from input.profiles and the temperature gradient is computed internally. The normalizing length is the plasma minor radius.

## DPHI0DR¶

Definition

The normalized equilibrium-scale radial electric field:

${\rm DPHI0DR} = \frac{\partial \Phi_0}{\partial r} \left( \frac{a e}{T_{\rm norm}} \right)$

such that

$E_r^{(0)} = -\frac{\partial \Phi_0}{\partial r} \nabla r$

• DEFAULT: 0.0

• When experimental profiles are used (PROFILE_MODEL = 2), this is computed internally from the profile parameters is in input.profiles and the normalizing length scale is the plasma minor radius. See also the parameter PROFILE_ERAD0_MODEL, which allows the simulation to be done with DPHI0DR = 0 regardless of the value in input.profiles.

• If sonic rotation effects are included (ROTATION_MODEL = 2), then this parameter is ignored and $$E_r^{(0)}$$ is assumed to be zero. With experimental profiles, this means that the $$E_r^{(0)}$$ in input.profiles is assumed to be the lowest-order field in sonic rotation theory, i.e. $$E_r^{(-1)}$$,and is used to compute the lowest-order sonic toroidal rotation parameters, OMEGA_ROT and OMEGA_ROT_DERIV.

## EPAR0¶

Definition

The normalized equilibrium-scale inductive electric field:

${\rm EPAR0} = \left< E_\| B \right> \left( \frac{a e}{T_{\rm norm} B_{\rm unit}} \right)$

• DEFAULT: 0.0

• In the neo theory module, the input $$\left< E_\| B \right>$$ is used directly.

• For the DKE, it into the RHS neoclassical source term as

${\rm v_\|} \left< E_\| B \right> \frac{B}{\left< B^2 \right>}$
• $$E_\|$$ is not presently in input.profiles. When experimental profiles are used (PROFILE_MODEL = 2), EPAR0 is read from input.neo and is assumed to be radially constant.

• For the Spitzer problem (SPITZER_MODEL = 1), use EPAR0_SPITZER instead.

## EPAR0_SPITZER¶

Definition

The normalized equilibrium-scale inductive electric field for use in the Spitzer problem:

${\rm EPAR0} = E_\varphi \left( \frac{a e}{T_{\rm norm}} \right)$

• DEFAULT: 1.0

• For the DKE, we assume that $$E_\varphi$$ is independent of $$\theta$$, such that $${\rm v}_\| E_\varphi = {\rm v}_\| {\rm EPAR0\_SPITZER}$$.

• This parameter is used only for the Spitzer problem (SPITZER_MODEL = 1). For the standard neoclassical problem, use EPAR0 instead.

## EQUILIBRIUM_MODEL¶

Definition

Parameter which selects the geometric equilibrium model.

Choices

• EQUILIBRIUM_MODEL = 0: s-alpha

• EQUILIBRIUM_MODEL = 1: large aspect ratio

• EQUILIBRIUM_MODEL = 2: Miller

• EQUILIBRIUM_MODEL = 3: General Grad-Shafranov

• DEFAULT: 0

• For experimental profiles (PROFILE_MODEL = 2), this parameter is ignored and the geometric equilibrium model is instead set by the parameter PROFILE_EQUILIBRIUM_MODEL.

• EQUILIBRIUM_MODEL=3 is available via interface. For this option, the number of Fourier coefficients, GEO_NY, must be a positive integer, with the corresponding Fourier coefficients set in GEO_YIN. For input.neo, these parameters are set by the file input.geo. Note that in addition to the fourier coefficients, the input equilibrium parameters RMIN_OVER_A, RMAJ_OVER_A, Q, SHEAR, BETA_STAR, BTCCW, and IPCCW must also be specified.

• See the geometry notes for more details about the geometric equilibrium models.

## GEO_NY¶

Definition

Number of Fourier coefficients for general Grad-Shafranov equilibrium.

• DEFAULT: 0

• This parameter is only available via subroutine interface and not by input.neo.

• This parameter is used only if EQUILIBRIUM_MODEL = 3. It must be a positive integer. The Fourier coefficient values themselves are specified by GEO_YIN.

• See the geometry notes for more details about the general geometry equilibrium model.

## GEO_YIN¶

Definition

Array of dimension (8,0:32) with the normalized Fourier coefficients $$\{a\_R,b\_R,a\_Z,b\_Z\}/a$$ and their radial derivatives $$\{a\_Rp,b\_Rp,a\_Zp,b\_Zp\}$$ for general Grad-Shafranov equilibrium.

• DEFAULT: 0.0

• This parameter is only available via subroutine interface and not by input.neo.

• This parameter is used only if EQUILIBRIUM_MODEL = 3. The number of Fourier coefficients is specified by GEO_NY and the coefficients are read-in as geo_yin(8,0:geo_ny).

• See the geometry notes for more details about the general geometry equilibrium model.

## IPCCW¶

Definition

Parameter which selects the orientation of the plasma current (and thus the poloidal magnetic field $$B_p$$) relative to the toroidal angle $$\varphi$$.

Choices

• IPCCW = 1: Counter-clockwise when viewed from above the torus - negative $$\hat{e}_{\varphi}$$ for the right-handed coordinate system $$(r,\theta,\varphi)$$. Thus, $$B_p$$ is oriented along the negative $$\hat{e}_{\varphi}$$ direction.

• IPCCW = -1: Clockwise when viewed from above the torus - positive $$\hat{e}_{\varphi}$$ for the right-handed coordinate system $$(r,\theta,\varphi)$$. Thus, $$B_p$$ is oriented along the positive $$\hat{e}_{\varphi}$$ direction.

• DEFAULT: -1

• In DIII-D, typically IPCCW = 1.

• When experimental profiles are used (PROFILE_MODEL = 2), the orientiation of IP is inferred from input.profiles.

## KAPPA¶

Definition

Elongation, $$\kappa$$, of the flux surface.

• DEFAULT: 1.0

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the elongation as a function of radius is read from input.profiles.

## MASS_*¶

Definition

The normalized mass:

${\rm MASS}\_* = m_{*}/m_{\rm norm}$

Commments

• DEFAULT: 1.0

• The mass of each species 1-11 is set as: MASS_1, MASS_2, MASS_3,…

• When experimental profiles are used (PROFILE_MODEL = 2), the normalizing mass is deuterium, $$m_{\rm norm}=m_{D}$$ = 3.3452e-27 kg

• The subroutine interface parameter is specified as a vector: neo_mass_in(1:11)

## N_ENERGY¶

Definition

The number of energy polynomials - 1 in the computational domain ($$n_{\varepsilon,\rm total}$$ = N_ENERGY+1).

• DEFAULT: 6

• The velocity-space coordinate $$x_a$$ is the normalized velocity: $$x_a = \sqrt{\varepsilon} = {\rm v}/(\sqrt{2}{\rm v}_{ta})$$.

• NEO uses an expansion of associated Laguerre polynomials in $$x_a$$, which is coupled with the Legendre expansion in $$\xi$$: $$P_l(\xi) L_m^{k(l)+1/2}(x_a^2)x_a^{k(l)}$$, where $$k(l)=0$$ for Legendre index $$l=0$$ and $$k(l)=1$$ for Legendre index $$l>0$$.

• The collocation integrals are formed from the monomial basis elements, $$x_a^{2m+k(l)}$$, which can be written in terms of Gamma and Beta functions.

Definition

The number of radial gridpoints, $$n_r$$ in the computational domain.

• DEFAULT: 1

• The radial grid is defined on the range RMIN_OVER_A $$\le r/a \le$$ RMIN_OVER_A_2. For a local simulation (PROFILE_MODEL = 1), the normalizing length scale $$a$$ is arbitrary. For a global simulation (PROFILE_MODEL = 2), $$a$$ is the plasma minor radius at the center of the radial simulation domain.

• N_RADIAL > 1 requires a global profile model (PROFILE_MODEL = 2). Otherwise, N_RADIAL = 1 and the profile model is local (PROFILE_MODEL = 1).

• For solution of only the first-order DKE, which is a radially-local problem, the radial grid is equally-spaced.

## N_SPECIES¶

Definition

The number of kinetic species.

• DEFAULT: 1

• The maximum allowed N_SPECIES is 11.

• Only one species with charge Z < 0 is allowed. If no species with Z < 0 is specified, then an adiabatic electron model is assumed.

• For local simulations (PROFILE_MODEL = 1), the order of the species and the normalizing density and temperature are arbitrary.

• For each species 1-N_SPECIES, Z_*, MASS_*, DENS_*, TEMP_*, DLNNDR_*, and DLNTDR_* are set in input.neo. The collision frequency with respect to species 1 (NU_1) is also set in input.neo.

• Quasi-neutrality is not checked.

• For experimental profiles (PROFILE_MODEL = 2), the normalizing mass is the mass of deuterium ($$m_D$$ = 3.3452e-27 kg), so the input masses should be given relative to this mass. The output quantities are normalized with respect to the density and temperature of the first species in input.neo and $$m_D$$, with $${\rm v}_{\rm norm} = \sqrt{T_{0,{\rm species 1}}/m_{D}}$$.

• The electron species, if kinetic, must be species number N_SPECIES in input.neo.

• Of the species-dependent parameters in input.neo, only Z_* and MASS_* are used, while DENS_*, TEMP_*, DLNNDR_*, DLNTDR_*, and NU_1 are determined from the parameters read from input.profiles.

• Quasi-neutrality is checked.

• See PROFILE_MODEL for more details.

## N_THETA¶

Definition

The number of theta gridpoints, $$n_\theta$$ in the computational domain.

• DEFAULT: 17

• N_THETA must be an odd number

• The theta grid range is equally-spaced and defined on the range $$-\pi \le \theta < \pi$$.

• The theta derivatives in the kinetic equation are treated with a 4th-order centered finite difference scheme. Periodic boundary conditions are assumed.

## N_XI¶

Definition

The number of xi polynomials - 1 in the computational domain ($$n_{\xi,\rm total}$$ = N_XI+1).

• DEFAULT: 17

• The velocity-space coordinate $$\xi$$ is the cosine of the pitch angle: $$\xi ={\rm v}_\|/{\rm v}$$.

• NEO uses an expansion of Legendre polynomials in $$\xi$$.

• The collocation integrals are done exactly analytically.

Definition

The normalized equilibrium-scale density of the electrons for the case of adiabatic electrons:

${\rm NE\_ADE} = \frac{n_{0,e}}{n_{\rm norm}}$

Commments

• DEFAULT: 1.0

• This paramter is used only if no species with Z < 0 is specified.

• When experimental profiles are used (PROFILE_MODEL = 2), the density as a function of radius is read from input.profiles and the normalizing density is the local density of Species 1, $$n_{\rm norm}(r)=n_{{\rm species 1}}$$.

## NU_1¶

Definition

The normalized collision frequency of the first kinetic species:

${\rm NU}\_1 = \frac{\tau_{11}^{-1}}{{\rm v}_{\rm norm}/a}$

where

$\tau_{ss}^{-1} = \frac{\sqrt{2} \pi e^4 z_s^4 n_{0s}}{m_s^{1/2} T_{0s}^{3/2}} {\rm ln} \Lambda$

• DEFAULT: 0.1

• Only the collision frequency for Species 1 is specified. The collision frequencies for the other species are computed internally in the code using NU_1, Z_*, MASS_*, DENS_*, and TEMP_*.

• When rotation effects are included (ROTATION_MODEL = 2), this parameter is the value at the outboard midplane ($$\theta = 0$$).

• When experimental profiles are used (PROFILE_MODEL = 2), this is computed internally from the profile parameters read from input.profiles. Also, the normalizing length scale is the plasma minor radius and the normalizing velocity is $${\rm v}_{\rm norm} = \sqrt{T_{\rm species1}/m_{D}}$$.

## OMEGA_ROT¶

Definition

The normalized toroidal angular frequency:

${\rm OMEGA\_ROT} = \frac{\omega_0}{{\rm v}_{\rm norm}/a}$

where $$\omega_0=-c\frac{d \Phi_{-1}}{d\psi}$$

• DEFAULT: 0.0

• Used only if sonic rotation effects are included (ROTATION_MODEL = 2).

• When experimental profiles are used (PROFILE_MODEL = 2), the toroidal angular frequency as a function of radius is read from input.profiles. The associated $$E_r$$ is assumed to be the lowest-order field, $$E_r^{(-1)}$$, and $$E_r^{(0)}$$ is assumed to be 0.

## OMEGA_ROT_DERIV¶

Definition

The normalized toroidal rotation shear:

${\rm OMEGA\_ROT\_DERIV} = \frac{d \omega_0}{d r}\frac{a^2}{{\rm v}_{\rm norm}}$

where $$\omega_0=-c\frac{d \Phi_{-1}}{d\psi}$$ is the torodial angular frequency.

• DEFAULT: 0.0

• Used only if sonic rotation effects are included (ROTATION_MODEL = 2).

• When experimental profiles are used (PROFILE_MODEL = 2), the toroidal angular frequency as a function of radius is read from input.profiles and its gradient is computed internally. The associated $$E_r$$ is assumed to be the lowest-order field, $$E_r^{(-1)}$$, and $$E_r^{(0)}$$ is assumed to be 0.

## PROFILE_DLNNDR_*_SCALE¶

Definition

Scaling factor for the normalized equilibrium-scale density gradient scale length in profile mode:

$a \frac{\partial {\rm ln} n_{0,*}}{\partial r} \rightarrow {\rm PROFILE\_DLNNDR\_*\_SCALE} \times \left(a \frac{\partial {\rm ln} n_{0,*}}{\partial r} \right)$

Commments

• DEFAULT: 1.0

• The scaling factor of each species 1-11 is set as: PROFILE_DLNNDR_1_SCALE, PROFILE_DLNNDR_2_SCALE, PROFILE_DLNNDR_3_SCALE,…

• This parameter is only used when experimental profiles are used (PROFILE_MODEL = 2). The density as a function of radius is read from input.profiles and the density gradient is computed internally. The normalizing length is the plasma minor radius. This gradient scale length is then re-scaled.

• The subroutine interface parameter is specified as a vector: neo_profile_dlnndr_scale_in(1:11)

## PROFILE_DLNTDR_*_SCALE¶

Definition

Scaling factor for the normalized equilibrium-scale temperature gradient scale length in profile mode:

$a \frac{d {\rm ln} T_{*}}{d r} \rightarrow {\rm PROFILE\_DLNTDR\_*\_SCALE} \times \left( a \frac{d {\rm ln} T_{*}}{d r} \right)$

Commments

• DEFAULT: 1.0

• The scaling factor of each species 1-11 is set as: PROFILE_DLNTDR_1_SCALE, PROFILE_DLNTDR_2_SCALE, PROFILE_DLNTDR_3_SCALE,…

• This parameter is only used when experimental profiles are used (PROFILE_MODEL = 2). The temperature as a function of radius is read from input.profiles and the temperature gradient is computed internally. The normalizing length is the plasma minor radius. This gradient scale length is then re-scaled.

• The subroutine interface parameter is specified as a vector: neo_profile_dlntdr_scale_in(1:11)

## PROFILE_EQUILIBRIUM_MODEL¶

Definition

Parameter which selects the geometric equilibrium model for experimental profiles.

Choices

• PROFILE_EQUILIBRIUM_MODEL = 1: Use Miller shaped geometry with the profiles of the geometric parameters as given in input.profiles.

• PROFILE_EQUILIBRIUM_MODEL = 2: Use the general Grad-Shafranov geometry with the fourier coefficients specified in input.profiles.geo.

• DEFAULT: 1

• Used only for experimental profiles (PROFILE_MODEL = 2)

• See the geometry notes for more details about the geometric equilibrium models.

Definition

Parameter which selects whether to include $$E_r^{(0)}$$ for experimental profiles.

Choices

• PROFILE_ERAD0_MODEL = 0: $$E_r^{(0)}$$ is set to zero regardless of the value in input.profiles.

• PROFILE_ERAD0_MODEL = 1: $$E_r^{(0)}$$ as specified in input.profiles is used.

• DEFAULT: 1

• Used only for experimental profiles (PROFILE_MODEL = 2).

• If sonic rotation effects are included (ROTATION_MODEL = 2) with experimental profiles, then this parameter is ignored and $$E_r^{(0)}$$ is assumed to be zero. This means that the $$E_r^{(0)}$$ in input.profiles is assumed to be the lowest-order field in sonic rotation theory, i.e. $$E_r^{(-1)}$$,and is used to compute the lowest-order sonic toroidal rotation parameters, OMEGA_ROT and OMEGA_ROT_DERIV.

## PROFILE_MODEL¶

Definition

Parameter which selects how the radial profile is defined.

Choices

• PROFILE_MODEL = 1: local (one radius)

• PROFILE_MODEL = 2: global, using experimental profiles

• DEFAULT: 1

• For PROFILE_MODEL = 1, N_RADIAL must be 1.

• The densities are set by DENS_* and quasi-neutrality is not checked.

• The temperatures are set by TEMP_*.

• For PROFILE_MODEL = 2, experimental profiles are defined in input.profiles. The number of radial gridpoints is specified by N_RADIAL.

• Additional models used for this case are specified by PROFILE_EQUILIBRIUM_MODEL and PROFILE_ERAD0_MODEL.

• Of the species-dependent parameters in input.neo, only Z_* and MASS_* are used for this case. The normalizing mass is the mass of deuterium ($$m_D$$ = 3.3452e-27 kg), so the input masses should be given relative to this mass. The output quantities are normalized with respect to the density and temperature of the first species in input.neo and $$m_D$$, with $${\rm v}_{\rm norm} = \sqrt{T_{0,{\rm species 1}}/m_{D}}$$.

• The electron species, if kinetic, must be species number N_SPECIES in input.neo.

• If the density profiles in input.profiles are not quasi-neutral, then the density profile of the first ion species is re-set.

## Q¶

Definition

Magnitude of the safety factor, $$|q|$$, of the flux surface:

$q(\psi) \doteq \frac{1}{2 \pi} \int_{0}^{2\pi} d\theta \; \frac{\mathbf{B} \cdot \nabla \varphi}{\mathbf{B} \cdot \nabla \theta}$

• DEFAULT: 2.0

• When experimental profiles are used (PROFILE_MODEL = 2), the safety factor as a function of radius is read from input.profiles.

• The orientation of the safety factor is determined by IPCCW and BTCCW.

## RHO_STAR¶

Definition

The ratio of the Larmor radius of the normalizing species to the normalizing length scale:

$\rho_* = \frac{\rho_{\rm norm}}{a} \; , {\rm where} \; \rho_{\rm norm} = \frac{c \sqrt{m_{\rm norm} T_{\rm norm}}}{e |B_{\rm unit}|}$

• DEFAULT: 0.001

• This parameter must be a positive number. The sign of $$B_{\rm unit}$$ is determined by IPCCW and BTCCW.

• When experimental profiles are used (PROFILE_MODEL = 2), $$\rho_*$$ is computed internally from the profile parameters in input.profiles and the normalizing length scale is the plasma minor radius.

## RMAJ_OVER_A¶

Definition

The ratio of the flux-surface-center major radius, $$R_0$$, to the normalizing length scale:math:a.

• DEFAULT: 3.0

• When experimental profiles are used (PROFILE_MODEL = 2), the flux-surface-center major radius as a function of radius, $$R_0(r)$$ is read from input.profiles and the normalizing length scale is the plasma minor radius.

## RMIN_OVER_A¶

Definition

The ratio of the midplane minor radius $$r$$ to the normalizing length scale:math:a.

• DEFAULT: 0.5

• For N_RADIAL > 1, this parameter is the lower bound of the radial grid.

## RMIN_OVER_A_2¶

Definition

The ratio of the midplane minor radius $$r$$ to the normalizing length scale:math:a.

• DEFAULT: 0.6

• For N_RADIAL > 1, this parameter is the upper bound of the radial grid.

• For N_RADIAL = 1, this parameter is not used.

## ROTATION_MODEL¶

Definition

Parameter which selects whether to solve the DKE in the diamagnetic ordering limit or in the sonic toroidal rotation ordering limit.

Choices

• ROTATION_MODEL = 1: sonic rotation effects not included (diamagnetic ordering assumed)

• ROTATION_MODEL = 2: sonic rotation effects included (solves the Hinton-Wong generalized DKE which allows for flow speeds on the order of the thermal speed).

• DEFAULT: 1

## S_DELTA¶

Definition

Measure of the rate of change of the average triangularity of the flux surface:

$s_\delta = r \frac{\partial \delta}{\partial r}$

• DEFAULT: 0.0

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the triangularity as a function of radius is read from input.profiles and the triangularity gradient is computed internally.

## S_KAPPA¶

Definition

Measure of the rate of change of the elongation of the flux surface:

$s_\kappa = \frac{r}{\kappa} \frac{\partial \kappa}{\partial r}$

• DEFAULT: 0.0

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the elongation as a function of radius is read from input.profiles and the elongation gradient is computed internally.

## S_ZETA¶

Definition

Measure of the rate of change of the squareness of the flux surface:

$s_\zeta = r \frac{\partial \zeta}{\partial r}$

• DEFAULT: 0.0

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the squareness as a function of radius is read from input.profiles and the squareness gradient is computed internally.

## S_ZMAG¶

Definition

Measure of the rate of change of the elevation of the flux surface:

$S_{Z0} = \frac{\partial Z_0}{\partial r}$

• DEFAULT: 0.0

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the flux-surface elevation as a function of radius, $$Z_0(r)$$, is read from input.profiles and its derivative is computed internally.

## SHEAR¶

Definition

Magnetic shear, $$s$$, of the flux surface:

$s = \frac{r}{q} \frac{\partial q}{\partial r}$

• DEFAULT: 1.0

• NOTE: This parameter is not used in the standard DKE equation! It is only used in the case of an anisotropic temperature species (e.g. ANISO_MODEL_* = 2) to compute $$d\Phi_*/dr$$.

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the safety factor as a function of radius is read from input.profiles and the safety factor gradient is computed internally.

## SHIFT¶

Definition

Shafranov shift, $$\Delta$$, of the flux surface:

$\Delta = \frac{\partial R_0}{\partial r}$

• DEFAULT: 0.0

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the flux-surface-center major radius as a function of radius, $$R_0(r)$$, is read from input.profiles and its derivative is computed internally.

## SILENT_FLAG¶

Definition

Parameter which selects how much data to print out.

Choices

• SILENT_FLAG = 0: output files are written.

• SILENT_FLAG > 0: no output files are written.

• DEFAULT: 0

## SIM_MODEL¶

Definition

Parameter which selects whether to determine the neoclassical transport from analytic theory or from numerical solution of the DKE.

Choices

• SIM_MODEL = 0: analytic theory only.

• SIM_MODEL = 1: numerical solution and analytic theory and NCLASS.

• SIM_MODEL = 2: numerical solution and analytic theory only.

• SIM_MODEL = 3: analytic theory and NCLASS only.

• SIM_MODEL = 4: neural network of NEO DKE solution.

• DEFAULT: 2

## SPITZER_MODEL¶

Definition

Parameter which selects whether to solve the standard neoclassical transport problem or the Spitzer problem.

Choices

• SPITZER_MODEL = 0: solve the standard neoclassical transport problem.

• SPITZER_MODEL = 1: solve the Spitzer problem.

• Must be run with an electron species and an ion species.

• The Spitzer coefficients (L11, L12, L21, L22) are output in the file out.neo.spitzer.

– DEFAULT: 0

Definition

The normalized equilibrium-scale temperature of the electrons for the case of adiabatic electrons:

${\rm TE\_ADE} = \frac{T_{0,e}}{T_{\rm norm}}$

Commments

• DEFAULT: 1.0

• This paramter is used only if no species with Z < 0 is specified.

• When experimental profiles are used (PROFILE_MODEL = 2), the temperature as a function of radius is read from input.profiles and the normalizing temperature is the local temperature of Species 1, $$T_{\rm norm}(r)=T_{{\rm species 1}}$$.

## TEMP_*¶

Definition

The normalized equilibrium-scale temperature:

${\rm TEMP}\_* = \frac{T_{0,*}}{T_{\rm norm}}$

Commments

• DEFAULT: 1.0

• The temperature of each species 1-11 is set as: TEMP_1, TEMP_2, TEMP_3,…

• When experimental profiles are used (PROFILE_MODEL = 2), the temperature as a function of radius is read from input.profiles and the normalizing temperature is the local temperature of Species 1, $$T_{\rm norm}(r)=T_{{\rm species 1}}$$.

• The subroutine interface parameter is specified as a vector: neo_temp_in(1:11)

## TEMP_PARA_*¶

Definition

The normalized equilibrium-scale parallel temperature:

${\rm TEMP\_PARA}\_* = \frac{T_{\|0,*}}{T_{\rm norm}}$

Commments

• DEFAULT: 1.0

• The parallel temperature of each species 1-11 is set as: TEMP_PARA_1, TEMP_PARA_2, TEMP_PARA_3,…

• This parameter is used only when the species’ anisotropic flag is set (ANISO_MODEL_* = 2).

• The subroutine interface parameter is specified as a vector: neo_temp_para_in(1:11)

## TEMP_PERP_*¶

Definition

The normalized equilibrium-scale perpendicular temperature:

${\rm TEMP\_PERP}\_* = \frac{T_{\perp,*}}{T_{\rm norm}}$

Commments

• DEFAULT: 1.0

• The perpendicular temperature of each species 1-11 is set as: TEMP_PERP_1, TEMP_PERP_2, TEMP_PERP_3,…

• This parameter is used only when the species’ anisotropic flag is set (ANISO_MODEL_* = 2).

• The subroutine interface parameter is specified as a vector: neo_temp_perp_in(1:11)

## THREED_MODEL¶

Definition

Parameter which selects whether to solve the DKE in toroidally axisymmetric limit (2D) or with nonaxisymmetric effects (3D).

Choices

• THREED_MODEL = 0: toroidally axisymmetric limit (2D).

• THREED_MODEL = 1: toroidally nonaxisymmetric effects are included (3D).

• This option is presently not available for experimental profiles (PROFILE_MODEL = 2).

• The local 3D equilibrium solver LE3 must be run first. All of the equilibrium parameters, including the spatial dimensions for $$(\theta,\varphi)$$, are read from the LE3 output file.

• Of the plasma equilibrium/geometry NEO input paramters, only RHO_STAR, DPHI0DR, and RMIN_OVER_A are used.

• Of the numerical resolution NEO input parameters, only N_XI and N_ENERGY are used.

• DEFAULT: 0

## THREED_EXB_MODEL¶

Definition

Parameter which selects whether to include the higher-order $${\bf E} \times {\bf B}$$ drift velocity in the DKE with nonaxisymmetric effects (3D).

Choices

• THREED_EXB_MODEL = 0: higher-order $${\bf E} \times {\bf B}$$ drift velocity not included.

• THREED_EXB_MODEL = 1: higher-order $${\bf E} \times {\bf B}$$ drift velocity included.

• Used only if toroidal nonaxisymmetric effects are included (THREED_MODEL = 1).

• The value of the equilibrium potential in the higher-order $${\bf E} \times {\bf B}$$ drift velocity is specified by THREED_EXB_DPHI0DR. Note that this does not affect the equilibrium potential in the neoclassical source term, which is specified by DPHI0DR.

• DEFAULT: 0

## THREED_EXB_DPHI0DR¶

Definition

The normalized equilibrium-scale radial electric field in the higher-order $${\bf E} \times {\bf B}$$ drift velocity:

${\rm THREED\_EXB\_DPHI0DR} = \frac{\partial \Phi_0}{\partial r} \left( \frac{a e}{T_{\rm norm}} \right)$

such that

$E_r^{(0)} = -\frac{\partial \Phi_0}{\partial r} \nabla r$

• DEFAULT: 0.0

• Used only if toroidal nonaxisymmetric effects (3D) are included (THREED_MODEL = 1).

• This does not affect the equilibrium potential in the neoclassical source term, which is specified by DPHI0DR.

## Z_*¶

Definition

The species’ charge.

Commments

• DEFAULT: 1.0

• The charge of each species 1-11 is set as: Z_1, Z_2, Z_3,…

• The subroutine interface parameter is specified as a vector: neo_z_in(1:11)

## ZETA¶

Definition

Squareness, $$\zeta$$, of the flux surface.

• DEFAULT: 0.0

• This is only active with EQUILIBRIUM_MODEL = 2 (the Miller equilibrium model).

• When experimental profiles are used (PROFILE_MODEL = 2), the squareness as a function of radius is read from input.profiles.

## ZMAG_OVER_A¶

Definition

The ratio of the elevation of the flux surface, $$Z_0$$, to the normalizing length scale $$a$$.

• When experimental profiles are used (PROFILE_MODEL = 2), the flux-surface elevation as a function of radius, $$Z_0(r)$$ is read from input.profiles and the normalizing length scale is the plasma minor radius.